The Cuttlebug Die Machine maximum die width is 6" or 5 15/16"
The Fiskars Self Healing Mat shims I used (made) are about 1/16" thick - 3 of them on top of each other is about 3/16" thick

The Solution...
Cut "one" long side off the 6" x 12" Accuquilt GO! Dies and the 6" x 12" Accuquilt GO! Top Die Cutting Mat.

(Note: I did this with the dies I recently purchased. Which are the 3 Circle 55012, 3 Hexagon 55011 and 5" Square 55010. The 5" Square die had one die knife that sits fairly close to where the die edge needs to be cut off. It can be cut down without hitting the edge of the die blade but be very careful when cutting this die down or any other die that has a die knife that rests close to where you need to cut die edge off.)

When I opened my 6" x 12" dies I decided to remove the green plastic shell that is glued to the actual wood die body. I thought if I removed the green plastic shell that the wood die body would then be small enough to fit though my Cuttlebug and that I could shim the wood die to make it thicker if needed. This did not work as the wood die body was still too wide and part of the wood peeled off and stayed on the green plastic thus making the back side of the wood die rough. So I heavily reglued the die back into the green plastic shell without a problem.

I decided that I would just trim a long edge off of each of the 6" x 12" dies using our stationary band saw. I decided that I should cut 3/8" of an inch off only ONE side of each die, this is so that I would have at least one truly straight side still left on the die. I picked the one side that does not have ID label on it.

I used a ruler and masking tape to mark my cut line on the die. (rubber side up - pic below). I measured exactly 3/8" of inch in from the side and I included the green plastic shell edge in that 3/8". You want to do this if you are using a band saw, scroll saw, jigsaw, etc. to help you keep your cut as straight as possible. (click pics to enlarge if you need to)

You can see in the picture below just how close I had to cut to the die knife when I cut the one side off the 5" Square die (each side of "this die" had the knifes running close to each edge - the other 2 dies I cut has plenty of room between the knifes and die edge). It took less than 5 minutes to alter each die that I had.

As you can see my cuts with the band saw were not perfectly straight. I am not too good with our band saw probably because it could use a new blade on it. They don't have to be perfectly straight. Just make sure they glide easily through the die machine with no side rubbing and that you only cut off one side of the die so that you always have a straight edge on the other side of the die as a guide. You will need to file down the cut edge of the die some as the plastic and wood may have a rough edge. Use sand paper or a rasp file to smooth the edges

(Picture below) One die with edge cut off inside my Cuttlebug Die Machine. Make sure your die does not drag on the sides of the machine when you test fit it and make sure your cut edge is smooth to prevent drag.

(Picture below) Now cut the Accuquilt 6" x 12" Top Cutting Mat down by 1/4" of an inch. Mask it off and use utility kitchen type scissors to do this. (the mat is slightly less wider than the dies and this is why you just need to cut off a 1/4")

(Picture below) I decided to make "shims" to use with the Accuquilt Dies as I did not want to use my Cuttlebug plexiglass cutting mats for this. I had an old Fiskers cutting mat that I cut 3 shims out of. The 3 shims go under the Accuquilt Die.

You can see the 6 large white muslin hexagon I cut with my Accuquilt Die and Cuttlebug laying on the table.

I should point out that if you go to accuquilt.com you can find which dies are 6" x 12" by reading if it requires the 6" x 12" top cutting mat. These dies will have to be cut down by you to work in your Cuttlebug. If the die requires the 5" x 10" top cutting mat, they can be used in the Cuttlebug without having to cut the die down nor the 5" x 10" top cutting mat down. You will have to bottom shim all the Accuquilt Dies when using them in the Cuttlebug. You may need more or less "shims" depending on how many layers of fabric you are cutting and the thickness of the fabric you are cutting.

If you have a different type of die cutting machine and if it has a 6" throat you can pretty well follow what I did here to get the dies to work in your die machine. You may have to cut off less than the 3/8" I had to cut off the Accuquilt Dies so that I could use them in my Cuttlebug.

One more note: I would assume that the new Accuquilt GO! Baby will have a die bed width of at least 6 5/16" up to 6 7/16" wide die bed so that it can handle the Accuquilt GO! 6" x 12" (6 5/16" x 12") dies.